**Problem Statement:**Three forces act on a pipe assembly:- \( F_1 = 50 \, \text{N} \)- \( F_2 = 80 \, \text{N} \)- Another force of \( 180 \, \text{N} \) is also shown.**Task:**Replace these forces with an equivalent resultant force and couple moment about point \( O \). Express the results in Cartesian vector form.**Solution:**- Resultant force \( \mathbf{R} = -210 \mathbf{k} \)- Couple moment \( \mathbf{M} = -15 \mathbf{i} + 225 \mathbf{j} \)**Diagram Explanation:**The diagram shows a three-dimensional pipe assembly with forces acting on it. The assembly consists of several straight segments connected at right angles. The configuration includes:- A vertical force of \( 180 \, \text{N} \) acting downward on a segment aligned parallel to the \( z \)-axis.- A horizontal force \( F_2 \) of \( 80 \, \text{N} \) acting along the \( y \)-axis.- A horizontal force \( F_1 \) of \( 50 \, \text{N} \) acting along the \( x \)-axis.Point \( O \) is marked as the point where the resultant force and couple moment need to be calculated. Distances are marked to help identify the lever arms for calculating moments:- The distance along the \( y \)-axis to where the \( 180 \, \text{N} \) force acts is \( 1.25 \, \text{m} \).- The horizontal distance \( 0.5 \, \text{m} \) to the force \( F_2 \).- The horizontal distance \( 0.75 \, \text{m} \) to the force \( F_1 \).

Total reaction at o is = -180 - 80 + 50 = -210 (Downward) R=-210k.

The three forces act on the pipe assembly. If F1 = 50 N and F2 = 80 N, replace this force system by an equivalent resultant force and couple moment acting at O. Express the result in Cartesian vector form. Solution R = -210 k, M = -15 i+ 225 j 180 N 1.25 m 0.5 m F1 0.75 m

The three forces act on the pipe assembly. If F1 = 50 N and F2 = 80 N, replace this force system by an equivalent resultant force and couple moment acting at O. Express the result in Cartesian vector form. Solution R = -210 k, M = -15 i+ 225 j 180 N 1.25 m 0.5 m F1 0.75 m

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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